x^2-2x-5=5x+3

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Solution for x^2-2x-5=5x+3 equation: 


Simplifying
x2 + -2x + -5 = 5x + 3

Reorder the terms:
-5 + -2x + x2 = 5x + 3

Reorder the terms:
-5 + -2x + x2 = 3 + 5x

Solving
-5 + -2x + x2 = 3 + 5x

Solving for variable 'x'.

Reorder the terms:
-5 + -3 + -2x + -5x + x2 = 3 + 5x + -3 + -5x

Combine like terms: -5 + -3 = -8
-8 + -2x + -5x + x2 = 3 + 5x + -3 + -5x

Combine like terms: -2x + -5x = -7x
-8 + -7x + x2 = 3 + 5x + -3 + -5x

Reorder the terms:
-8 + -7x + x2 = 3 + -3 + 5x + -5x

Combine like terms: 3 + -3 = 0
-8 + -7x + x2 = 0 + 5x + -5x
-8 + -7x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-8 + -7x + x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1, 8}

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